a) $\left(7\cdot {10}^6\right)\cdot \left(1,1\cdot {10}^5\right)=7\cdot {10}^6\cdot 1,1\cdot {10}^5=7\cdot 1,1\cdot {10}^6\cdot {10}^5=7,7\cdot {10}^{6+5}=7,7\cdot {10}^{11}$  

b)  $\left(2\cdot {10}^{-8}\right)\cdot \left(3,8\cdot {10}^6\right)=2\cdot {10}^{-8}\cdot 3,8\cdot {10}^6=7,6\cdot {10}^{\left(-8\right)+6}=7,6\cdot {10}^{-2}$

c) $\left(9,6\cdot {10}^{-7}\right)\cdot \left(2\cdot {10}^{-2}\right)=9,6\cdot 2\cdot {10}^{-7}\cdot {10}^{-2}=19,2\cdot {10}^{\left(-7\right)+\left(-2\right)}=1,92\cdot 10\cdot {10}^{-9}=1,92\cdot {10}^1\cdot {10}^{-9}=1,92\cdot {10}^{1+\left(-9\right)}=1,92\cdot {10}^{-8}$  

d) ${\left(4\cdot {10}^{10}\right)}^3=4^3\cdot {\left({10}^{10}\right)}^3=64\cdot {10}^{10\cdot 3}=6,4\cdot 10\cdot {10}^{30}=6,4\cdot {10}^1\cdot {10}^{30}=6,4\cdot {10}^{1+30}=6,4\cdot {10}^{31}$  

e) ${\left(0,8\cdot {10}^{-8}\right)}^2={0,8}^2\cdot {\left({10}^{-8}\right)}^2=0,64\cdot {10}^{\left(-8\right)\cdot 2}=6,4\cdot {10}^{-1}\cdot {10}^{-16}=6,4\cdot {10}^{\left(-1\right)+\left(-16\right)}=6,4\cdot {10}^{-17}$  

f) $\frac{7,5\cdot {10}^{15}}{8\cdot {10}^8}=\frac{7,5}{8}\cdot \frac{{10}^{15}}{{10}^8}=0,9375\cdot {10}^{15-8}=9,375\cdot {10}^{-1}\cdot {10}^7=9,375\cdot {10}^{-1+7}=9,375\cdot {10}^6$  

g)  $\left(7\cdot {10}^{13}\right):\left(2\cdot {10}^{-10}\right)=\frac{7\cdot {10}^{13}}{2\cdot {10}^{-10}}=\frac{7}{2}\cdot \frac{{10}^{13}}{{10}^{-10}}=3,5\cdot {10}^{13-\left(-10\right)}=3,5\cdot {10}^{23}$  

h)  $\left(7,4\cdot {10}^{25}\right):\left(2\cdot {10}^{18}\right)=\frac{7,4\cdot {10}^{25}}{2\cdot {10}^{18}}=\frac{7,4}{2}\cdot \frac{{10}^{25}}{{10}^{18}}=3,7\cdot {10}^{25-18}=3,7\cdot {10}^7$

i) $\left(5,1\cdot {10}^{-25}\right):\left(1,7\cdot {10}^{15}\right)=\frac{5,1\cdot {10}^{-25}}{1,7\cdot {10}^{15}}=\frac{5,1}{1,7}\cdot \frac{{10}^{-25}}{{10}^{15}}=3\cdot {10}^{-25-15}=3\cdot {10}^{-40}$